Practice Questions
Concept Explanation
Permutations count arrangements of objects where order matters. Selecting r objects from n distinct objects and arranging them gives nPr.
Key Formulas
- nPr = n! / (n − r)!
- Arrangements of n distinct objects in a row = n!
- nP0 = 1, nPn = n!
Example
6P2 = 6!/4! = 6 × 5 = 30.
Common Trap
Permutation applies when order matters; do not use nCr for ranking problems.
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Q1 Easy
In how many ways can 5 books be arranged on a shelf?
Explanation5! = 120 arrangements. -
Q2 Easy
How many 2-letter arrangements from {A,B,C,D,E} without repetition?
Explanation5P2 = 5 × 4 = 20. -
Q3 Medium
6P3 equals:
Explanation6P3 = 6 × 5 × 4 = 120. -
Q4 Easy
In how many ways can 4 people stand in a queue?
Explanation4! = 24. -
Q5 Medium
8P2 equals:
Explanation8 × 7 = 56. -
Q6 Hard
How many ways to award 1st, 2nd, 3rd prizes to 10 contestants?
Explanation10P3 = 10 × 9 × 8 = 720. -
Q7 Easy
7P1 equals:
Explanation7P1 = 7.
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Q8 Medium
How many 4-digit arrangements using 1,2,3,4,5 without repetition?
Explanation5P4 = 5 × 4 × 3 × 2 = 120. -
Q9 Hard
9P4 equals:
Explanation9 × 8 × 7 × 6 = 3024. -
Q10 Medium
In how many ways can 3 students be seated in 8 chairs (one per chair)?
Explanation8P3 = 8 × 7 × 6 = 336. -
Q11 Easy
10P2 equals:
Explanation10 × 9 = 90. -
Q12 Easy
How many ways to arrange the letters of the word DOG?
Explanation3 distinct letters: 3! = 6. -
Q13 Easy
5P5 equals:
Explanation5P5 = 5! = 120. -
Q14 Medium
How many ways can 6 runners finish 1st and 2nd?
Explanation6P2 = 30.
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DS1 Easy
How many ways can 5 distinct books be arranged?
Statement IAll 5 books are used.
Statement IIOrder on the shelf matters.
ExplanationStatement I alone: 5! = 120 arrangements. -
DS2 Medium
How many 2-person arrangements from 8 people?
Statement INo person is repeated.
Statement IIOrder of the two matters.
ExplanationNeed both: 8P2 = 56.
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DS3 Easy
What is the value of nPr?
Statement In = 7 and r = 3.
Statement IInPr = 210.
ExplanationEach gives 7P3 = 210. -
DS4 Hard
Can the number of arrangements be found?
Statement I6 distinct objects are arranged in a row.
Statement IIExactly 4 positions are filled.
ExplanationStatement I alone: 6! = 720. II changes the problem to 6P4 = 360.